Minimization of functions having Lipschitz continuous first partial derivatives.

By L. Armijo. 1966

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In Mathematical Optimization

Citations in the corpus

Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates (2019, methodology): “Armijo line-search [3] is a standard method for setting the step-size for gradient descent in the deterministic setting [61].”
Learning Rate Adaptation in Stochastic Gradient Descent (2001, background): “(2.6) The main feature of the proposed learning rate adaptation scheme is that it exploits gradient–related information from the current as well as the two previous pattern presentations.”
Why Gradient Clipping Accelerates Training: A Theoretical Justification for Adaptivity (2019, background): “Armijo (1966) proposed the famous backtracking line search algorithm to choose step size dynamically.”
Why are Adaptive Methods Good for Attention Models? (2020, background): “Adaptive step sizes during optimization have long been studied [3, 21].”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, background): “The first criterion (2.4) is sometimes called the Armijo condition [9] [192].”
Policy gradient in Lipschitz Markov Decision Processes (2015, methodology): “Such result is simply obtained by the maximization w.r.t. the step size of the following quadratic lower bound to the performance improvement derived 3 See (Armijo 1966) for conditions under which convergence occurs and a proof of convergence. from Lemma 8 using the L2-norm as metric: J θ t+1μ − J θ”
A Stochastic Line Search Method with Convergence Rate Analysis (2018, background): “One popular line-search criteria specifies an acceptable step length should give sufficient decrease in the objective function f : (Armijo condition [1]) f(xk + αdk) ≤ f(xk)− θα ‖∇f(xk)‖(2) , (1.”
Stochastic Adaptive Line Search for Differentially Private Optimization (2020, methodology): “Armijo line search [9], [10] is a classical technique to find a step size η that gives sufficient reduction in the objective function f .”
Optimal mode-switching for hybrid systems with varying initial states (2008, methodology): “For each Xi we will moreover find the optimal a ⋆ i by executing a gradient descent algorithm with Armijo step size [1], under the assumption that Xi has N (i) elements, i.”
Conjugate Gradient Methods with Armijo-type Line Searches (2002, methodology): “In this paper, we will propose two Armijo-type searches, both of which are based on the standard Armijo line search (see [ 2 ]).”
Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems (2008, unknown): “(21), cm(λ;i)−1(λ) < cm(λ;i)(λ); and by the definition of the curve, cm(λ;i)−1(λ) = cm(λ;i)−1(0).”